# Tensor Product

In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the most general bilinear operation. In some contexts, this product is also referred to as outer product. The term "tensor product" is also used in relation to monoidal categories.

### Other articles related to "tensor product, tensors, tensor, product":

Littelmann Path Model - Background and Motivation
... For two highest weights λ, μ, find the decomposition of their tensor product L(λ) L(μ) into irreducible representations ... Moreover, the Levi branching problem can be embedded in the tensor product problem as a certain limiting case.) Answers to these questions were first provided by Hermann Weyl and Richard Brauer ... The celebrated Littlewood-Richardson rule that describes both tensor product decompositions and branching from m+n to m n in terms of lattice permutations of skew tableaux ...
Tensor Product Network
... A tensor product network, in neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable assignment ... the ideas (such as variable names and target assignments), and the tensor product of these vectors construct a network whose mathematical properties allow the user to easily extract the association ... Ranked Tensors A rank 2 tensor can store an arbitrary binary relation Similarly, regard the binding units as a matrix B, and the filler and variable as column vectors f and v ...
Tensor Product For Computer Programmers - Array Programming Languages
... For example, in APL the tensor product is expressed as (for example or ) ... In J the tensor product is the dyadic form of */ (for example a */ b or a */ b */ c) ... Note that J's treatment also allows the representation of some tensor fields, as a and b may be functions instead of constants ...
Positive-definite Kernel - Examples - Direct Sum and Tensor Product
... For the tensor product, a suitable kernel is defined on the Cartesian product X × Y in a way that extends the Schur product of positive matrices This positive kernel gives the tensor ...
Tate Twist
... V(1), is the representation on the tensor product V⊗Qp(1), where Qp(1) is the p-adic cyclotomic character (i.e ... m is a positive integer, the mth Tate twist of V, denoted V(m), is the tensor product of V with the m-fold tensor product of Qp(1) ...

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